In an expanding class of applications, accurate simulations across multiple spatial and temporal scales is necessary for design and analysis purposes. We investigate an atomistic-to-continuum (AtC) concurrent coupling method to couple our h-adaptive spacetime discontinuous Galerkin (SDG) for continuum elastodynamics to an atomistic discontinuous Galerkin (ADG) method for particle dynamics. The formulation couples non-overlapping continuum and atomistic models across a sharp interface in a mathematically consistent fashion. We show that the AtC method is able to pass mechanical signals across the material interface without damping or energy loss. Numerical examples also demonstrate the ability of the h-adaptive SDG method to reconcile disparate time steps while resolving the atomistic signal in the continuum.